Question

the graph of a function g is shown below. use the graph of the function to find its average rate of change from x = - 8 to x = 4. simplify your answer as much as possible.

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = g(x)$ from $x = a$ to $x = b$ is given by $\frac{g(b)-g(a)}{b - a}$. Here, $a=-8$ and $b = 4$.

Step2: Find $g(-8)$ and $g(4)$ from the graph

From the graph, when $x=-8$, $g(-8)= - 4$; when $x = 4$, $g(4)=-4$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{g(4)-g(-8)}{4-(-8)}=\frac{-4-(-4)}{4 + 8}=\frac{-4 + 4}{12}=\frac{0}{12}=0$.

Answer:

$0$